Spatial collinear restricted four-body problem with repulsive Manev potential

We outline some aspects of the dynamics of an infinitesimal mass under the Newtonian attraction of three point masses in a symmetric collinear relative equilibria configuration when a repulsive Manev potential (\(-1/r +e/r^{2}\)), \(e>0\), is applied to the central mass. We investigate the relative equilibria of the infinitesimal mass and their linear stability as a function of the mass parameter \(\beta \), the ratio of mass of the central body to the mass of one of two remaining bodies, and e. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass.     

Evidence for Amazonian acidic liquid water on Mars—A reinterpretation of MER mission results

The Mars Exploration Rover (MER) missions have confirmed aqueous activity on Mars. Here we review the analyses of the field-based MER data, and conclude that some weathering processes in Meridiani Planum and Gusev crater are better explained by late diagenetic water-rock interactions than by early diagenesis only. At Meridiani, the discovery of jarosite by MER-1 Opportunity indicates acidic aqueous activity, evaporation, and desiccation of rock materials. MER-based information, placed into the context of published data, point to local and limited aqueous activity during geologically recent times in Meridiani. Pre-Amazonian environmental changes (including important variations in the near-surface groundwater reservoirs, impact cratering, and global dust storms and other pervasive wind-related erosion) are too extreme for pulverulent jarosite to survive over extended time periods, and therefore we argue instead that jarosite deposits must have formed in a climatically more stable period. Any deposits of pre-existent concretionary jarosite surviving up to the Amazonian would not have reached completion in the highly saline and acidic brines occurring at Meridiani. MER-2 Spirit has also revealed evidence for local and limited Amazonian aqueous environmental conditions in Gusev crater, including chemical weathering leading to goethite and hematite precipitation, rock layering, and chemical enhancement of Cl, S, Br, and oxidized iron in rocks and soils. The estimated relative age of the impact crater materials in Gusev indicates that these processes have taken place during the last 2 billion years. We conclude that minor amounts of shallow acidic liquid water have been present on the surface of Mars at local scales during the Amazonian Period.     

Hip-hop solutions of the 2N-body problem

Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.     

Three-Dimensional p–q Resonant Orbits Close to Second Species Solutions

The purpose of this paper is to study, for small values of , the three-dimensional p–q resonant orbits that are close to periodic second species solutions (SSS) of the restricted three-body problem. The work is based on an analytic study of the in- and out-maps. These maps are associated to follow, under the flow of the problem, initial conditions on a sphere of radius around the small primary, and consider the images of those initial points on the same sphere. The out-map is associated to follow the flow forward in time and the in-map backwards. For both mappings we give analytical expressions in powers of the mass parameter. Once these expressions are obtained, we proceed to the study of the matching equations between both, obtaining initial conditions of orbits that will be 'periodic' with an error of the order ^1–, for some (1/3,1/2). Since, as 0, the inner solution and the outer solution will collide with the small primary, these orbits will be close to SSS.     

Influence of Decarbonisation and Phosphate Dosage on Copper Corrosion in Drinking Water Systems

The effect of softening/decarbonisation and dosage of orthophosphate on copper corrosion was studied in pipe rigs according to the German standard DIN 50931, part 1. A literature study with regard to the effects of phosphate dosing on copper corrosion has shown that on the one hand and in most of the cases a dosage of phosphate led to lower copper concentrations. On the other hand phosphate aggravated the copper corrosion in some cases. The mechanisms are not yet clear and the influence of phosphate on the corrosion of copper remains a question to be answered. Using standardised on‐site corrosion tests (DIN 50931‐1) with virgin copper pipes softening/decarbonisation has decreased the copper concentration. Two effects of phosphate on copper corrosion were noticed: Phosphate dosing decreased the copper oxidation and resulted in lower copper concentration in water. Likewise phosphate hindered the precipitation of cupric ions, which prolonged the existence of copper in water and resulted in a higher copper concentration. As a consequence, dosing phosphate can decrease or increase the copper corrosion, this depends on which effect is dominating.     

Centimeter repeatability of the VLBI estimates of European baselines

Summary In the last three years, the European Geodetic Very Long Baseline Interferometry (VLBI) Network has grown to a total of six fixed antennas placed in Germany, Italy, Spain and Sweden, all equipped with the standard geodetic VLBI instrumentation and data recording systems. During this period of time, several experiments have been carried out using this interferometer providing data of very high quality due to the excellent sensitivity and performance of the European stations. The purpose of this paper is to study the consistency of the VLBI geodetic results on the European baselines with respect to the different degrees of freedom in the analysis procedure. In order to complete this study we have made use of both real and simulated data sets, two different software packages (OCCAM 3.0 and CALC 7.4/SOLVE) and a variety of strategies in the data analysis. The results we have obtained show that the repeatability of the VLBI estimates of the baseline lengths in the European network is better than one centimeter, independent of the different analysis methods, and is consistent with the formal error levels expected from the data analysis. This consistency should be enough to produce geophysically significant information in Europe from VLBI data within a relatively short time span.     

First identification and characterization of Borrobol‐type tephra in the Greenland ice cores: new deposits and improved age estimates

Contiguous sampling of ice spanning key intervals of the deglaciation from the Greenland ice cores of NGRIP, GRIP and NEEM has revealed three new silicic cryptotephra deposits that are geochemically similar to the well‐known Borrobol Tephra (BT). The BT is complex and confounded by the younger closely timed and compositionally similar Penifiler Tephra (PT). Two of the deposits found in the ice are in Greenland Interstadial 1e (GI‐1e) and an older deposit is found in Greenland Stadial 2.1 (GS‐2.1). Until now, the BT was confined to GI‐1‐equivalent lacustrine sequences in the British Isles, Sweden and Germany, and our discovery in Greenland ice extends its distribution and geochemical composition. However, the two cryptotephras that fall within GI‐1e ice cannot be separated on the basis of geochemistry and are dated to 14358 ± 177 a b2k and 14252 ± 173 a b2k, just 106 ± 3 years apart. The older deposit is consistent with BT age estimates derived from Scottish sites, while the younger deposit overlaps with both BT and PT age estimates. We suggest that either the BT in Northern European terrestrial sequences represents an amalgamation of tephra from both of the GI‐1e events identified in the ice‐cores or that it relates to just one of the ice‐core events. A firm correlation cannot be established at present due to their strong geochemical similarities. The older tephra horizon, found within all three ice‐cores and dated to 17326 ± 319 a b2k, can be correlated to a known layer within marine sediment cores from the North Iceland Shelf (ca. 17179‐16754 cal a BP). Despite showing similarities to the BT, this deposit can be distinguished on the basis of lower CaO and TiO₂ and is a valuable new tie‐point that could eventually be used in high‐resolution marine records to compare the climate signals from the ocean and atmosphere.     

Pseudo-nitzschia spp. (Bacillariophyceae) and dissolved organic matter (DOM) dynamics in the Ebro Delta (Alfacs Bay, NW Mediterranean Sea)

Samples were collected during one annual cycle (April 2007–March 2008) at Alfacs Bay (NW Mediterranean Sea) central station in order to assess the influence of organic nutrients in the growth of the microalgae assemblage, with special reference to Pseudo-nitzschia spp. This potentially toxic diatom forms natural and recurrent blooms in the study area. To assess further the relationship between Pseudo-nitzschia spp. and nutrients an enrichment experiment with high molecular weight dissolved organic matter (HMWDOM) was performed with field samples obtained during a Pseudo-nitzschia spp. bloom. HMWDOM was extracted from water collected at Alfacs Bay. Five bioassays were prepared: N + P (seawater with addition of nitrate and phosphate), DOM (addition of HMWDOM), (−N + P) + DOM (nitrogen deficient, with addition of phosphate and HMWDOM), (N + P) + DOM (addition of nitrate, phosphate and HMWDOM), seawater control (without added nutrients), and B + DOM (control of bacteria, without microalgae). The experiment was run in batch mode over 4 days. Results from the field study revealed that the concentrations of organic nutrients mostly surpassed the inorganic pool. Pseudo-nitzschia spp. was the most frequent and abundant taxa of the microalgae community. The micro-planktonic assemblage was arranged according to a seasonal factor (ANOSIM and cluster analysis). DON, nitrate and silicate were the most important abiotic parameters contributing to the dissimilarities between seasons (SIMPER analysis) and thereby potentially influencing the seasonal distribution of microalgae in the representative station. In the experimental investigation, Pseudo-nitzschia cells increased by the end of the experiment in the DOM bioassay but no respective increase was observed for chlorophyll a. This could point to an acquisition of nutrients through the DOM fraction that would conjointly reduce the need of chlorophyll a. The data obtained suggest that organic nutrients may exert an important role in the development of microalgae, including Pseudo-nitzschia spp., in the selected location.     

Coastal inshore waters in the NW Mediterranean: Physicochemical and biological characterization and management implications

The physicochemical and biological characteristics of coastal waters form a gradient extending from land to ocean. In the Mediterranean this gradient is particularly large, due to the sea’s weak tides. Within coastal waters, those waters in contact with land are called coastal inshore waters (CIW), defined herein as between 0 and 200 m from the shoreline. Here we present the first physicochemical and biological characterization of CIW of the NW Mediterranean Sea. This case study is based on 19 years of data collected from coastal inshore (CIW; 0–200 m), nearshore (CNW; 200–1500 m), and offshore (COW; >1500 m) waters of the Catalan coast. Analyses of these data showed that the physicochemical and biological characteristics of CIW differ significantly from those of CNW and COW due to: (1) significantly higher concentrations of dissolved inorganic nutrients (nitrate = 11.07 μM, nitrite = 0.52 μM, ammonium = 6.43 μM, phosphate = 0.92 μM, silicates = 5.99 μM) and chlorophyll-a (=2.42 μg/L) in CIW than in either CNW or COW (in some cases up to one order of magnitude); (2) a greater variability of dissolved inorganic nutrients and chlorophyll-a in CIW than in CNW and COW, and (3) the presence of a mostly urban population and the effects of river inflows as a primary source of CIW variability but with minimal impact on CNW or COW. In addition, the risk of eutrophication was found to be highest in CIW, placing human and environmental interests at greater risk than in the outermost coastal waters. The results highlight the importance of considering the distinctive physicochemical and biological properties of CIW in future coastal waters studies. This is of major importance in assessments of eutrophication and coastal water quality, not only to identify the pressure–impact relationships but also to allow the timely detection of local environmental problems and thus avoid endangering the unique communities of CIW and ensuring the sustainability of human activities. In conclusion, CIW characterization is essential to integrate coastal zone management.     

The natural attenuation of two acidic effluents in Tharsis and La Zarza-Perrunal mines (Iberian Pyrite Belt, Huelva, Spain)

The geochemical evolution of two acid mine effluents in Tharsis and La Zarza-Perrunal mines (Iberian Pyrite Belt, Huelva, Spain) has been investigated. In origin, these waters present a low pH (2.2 and 3.1) and high concentrations of dissolved sulphate and metals (Fe, Al, Mn, Cu, Zn, As, Cd, Co, Cr, Ni). However, the natural evolution of these acidic waters (which includes the bacterial oxidation of Fe(II) and the subsequent precipitation of Fe(III) minerals) represents an efficient mechanism of attenuation. This self-mitigating process is evidenced by the formation of schwertmannite, which retains most of the iron load and, by sorption, toxic trace elements like As. The later mixing with pristine waters rises the pH and favours the total precipitation of Fe(III) at pH 3.5 and, subsequently, Al compounds at pH 4.5, along with the sorption of trace metals (Mn, Zn, Cu, Cd, Co, Ni) until chemical equilibrium at circumneutral conditions is achieved.